Finite Group Databasebeta

← Group #295721

Character table — Group #295721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888822444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111-1-1111-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111
χ511111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111
χ611111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-11111-1-1
χ711111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ811111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ91111111111111111-1-1-1-111-11111-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-11-1
χ101111111111111111-1-1-1-111-11111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-11
χ111111111111111111-1-1-1-111-111-1-1-111111111-1-1-1-11111-1-1-1-111-11-1-1-1-1-1-111-11
χ121111111111111111-1-1-1-111-111-1-1-11111-1-1-1-11111-1-1-1-1111111-11-1-1-1-111-1-11-1
χ131111111111111111-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-111-1-1-1-1111-1
χ141111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1111-1-1111-1
χ172222222222-2-2-222-22222-2-2-20022-200220000000000000000000-2-2000000000
χ182222222222-2-2-222-22222-2-2-200-2-2-200-2-2000000000000000000022000000000
χ192222222222-2-2-222-2-2-2-2-2-2-220022200-2-200000000000000000002-2000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2200-2-2200220000000000000000000-22000000000
χ2122222222-2-2222-2-2222-2-2-2-2-222002-2-200000000000000000000-200200000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-20022200000000000000000000200-200000000
χ2322222222-2-2222-2-22-2-222-2-222200-2-2-200000000000000000000200-200000000
χ2422222222-2-2222-2-22-2-222-2-22-2-200-22200000000000000000000-200200000000
χ2522222222-2-2-2-2-2-2-2-222-2-22220000-2000000000000000000002-200002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-22220000-200000000000000000000-220000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-200002000000000000000000002-20000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-20000200000000000000000000-2200002-2000000
χ29222-2-22-2-22-22-2-22-2200002-202i−2i0002i−2i00000022-2-200002i2i−2i−2i00000000000000
χ30222-2-22-2-22-22-2-22-2200002-202i−2i0002i−2i000000-2-2220000−2i−2i2i2i00000000000000
χ31222-2-22-2-22-22-2-22-2200002-20−2i2i000−2i2i00000022-2-20000−2i−2i2i2i00000000000000
χ32222-2-22-2-22-22-2-22-2200002-20−2i2i000−2i2i000000-2-22200002i2i−2i−2i00000000000000
χ33222-2-22-2-2-222-2-2-2220000-2202i−2i000−2i2i0022-2-200002i2i−2i−2i000000000000000000
χ34222-2-22-2-2-222-2-2-2220000-2202i−2i000−2i2i00-2-2220000−2i−2i2i2i000000000000000000
χ35222-2-22-2-2-222-2-2-2220000-220−2i2i0002i−2i0022-2-20000−2i−2i2i2i000000000000000000
χ36222-2-22-2-2-222-2-2-2220000-220−2i2i0002i−2i00-2-22200002i2i−2i−2i000000000000000000
χ3722-2-22-2-222-2000-2202i−2i2i−2i000002i−2i0002-2000000002−22−2i2−i2i2−i200000000i2−i22−200
χ3822-2-22-2-222-2000-2202i−2i2i−2i000002i−2i0002-200000000−22−22−i2i2−i2i200000000−i2i2−2200
χ3922-2-22-2-222-2000-2202i−2i2i−2i00000−2i2i000-22000000002−22−2i2−i2i2−i200000000−i2i2−2200
χ4022-2-22-2-222-2000-2202i−2i2i−2i00000−2i2i000-2200000000−22−22−i2i2−i2i200000000i2−i22−200
χ4122-2-22-2-222-2000-220−2i2i−2i2i000002i−2i000-22000000002−22−2−i2i2−i2i200000000i2−i2−2200
χ4222-2-22-2-222-2000-220−2i2i−2i2i000002i−2i000-2200000000−22−22i2−i2i2−i200000000−i2i22−200
χ4322-2-22-2-222-2000-220−2i2i−2i2i00000−2i2i0002-2000000002−22−2−i2i2−i2i200000000−i2i22−200
χ4422-2-22-2-222-2000-220−2i2i−2i2i00000−2i2i0002-200000000−22−22i2−i2i2−i200000000i2−i2−2200
χ45444-4-44-4-44-4-4444-4-40000-440000000000000000000000000000000000000000
χ46444-4-44-4-4-44-444-44-400004-40000000000000000000000000000000000000000
χ4744-44-4-44-444000-4-40000000000000000000000000000022−22−222200000000000000
χ4844-44-4-44-444000-4-400000000000000000000000000000−222222−2200000000000000
χ4944-44-4-44-4-4-40004400000000000000000000000002i2−2i2−2i22i2000000000000000000
χ5044-44-4-44-4-4-4000440000000000000000000000000−2i22i22i2−2i2000000000000000000
χ5144-4-44-4-44-440004-404i−4i−4i4i000000000000000000000000000000000000000000
χ5244-4-44-4-44-440004-40−4i4i4i−4i000000000000000000000000000000000000000000
χ534-4-44-44-440044-400-4000000000000000000002i2−2i22i2−2i20000000000000000000000
χ544-4-44-44-440044-400-400000000000000000000−2i22i2−2i22i20000000000000000000000
χ554-4-44-44-4400-4-44004000000000000000022−2222−2200000000000000000000000000
χ564-4-44-44-4400-4-440040000000000000000−2222−222200000000000000000000000000
χ574-4-4-4444-4004-4400-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ584-4-4-4444-4004-4400-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ594-4-4-4444-400-44-4004000000000000000022−22−222200000000000000000000000000
χ604-4-4-4444-400-44-40040000000000000000−222222−2200000000000000000000000000
χ618-8888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-8-888000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).